The present invention relates to instruments for generating precision measurements of time intervals between measured events in pulse streams, and more particularly to characterizing noise in repetitive waveforms.
The semiconductor industry is continually striving to satisfy demands for higher data processing speeds, in connection with complex computers, high definition video graphics, telecommunications, and other fields that place a high premium on rapid trasfer of large amounts of data. Microprocessor systems move data at speeds based on high frequency clocks that determine the rate at which signals are clocked through semiconductor circuitry. During this decade, typical clock frequencies have increased from about 33 MHz to about 200 MHz, and semiconductor devices currently under development are expected to operate under clock frequencies that exceed 1 billion Hz.
Typical microprocessors can have from 256 to 512 connector pins or pads for the input and output of data Clocked signals exit the device through as many as 100 of the connector pins, and it is imperative to know the relationship of each clocked pulse to the pulses on the other output pins. Irregular timing, if not corrected, can cause errors in the semiconductor device.
When timing signals at higher frequencies, it becomes increasingly important to analyze, and if possible reduce, the intrinsic noise components of data and clock signals. This noise is known by several terms including jitter, wander, unintended modulation, and phase noise. Jitter, as such noise is referred to herein, concerns the instability of pulse streams, especially repetitive waveforms. Ideally, repetitive pulse ses are absolutely stable, in that each individual pulse or cycle has the same width or duration. Jitter represents a deviation, perhaps in picoseconds, from the ideal. As clock frequencies within semiconductor devices and other high speed applications increase, the jitter component becomes more pronounced. In high definition video graphic chips, jitter can cause a flicker or jumping of the video image. Jitter can cause glitches in audio devices, and disparity between output and input serial data in network applications. Nowadays, many semiconductors are designed to allow no more than a 500 picosecond (i.e. 500 trillionth of a second) error between one output pin and another. Tolerances in high definition video applications are more stringent, e.g. as low as 100 picoseconds. Accordingly, measurements of jitter and other aspects of timing are critical during the prototyping and development stages of semiconductor devices.
Therefore, it is an object of the present invention to provide an apparatus and method for more accurately characterizing the noise component of data and clock signals.
Another object is to provide a process for measuring and characterizing jitter in a manner that reduces jitter contributed by the measurement system.
A further object is to provide a system for sampling a waveform in a manner that improves the distinction between true noise frequencies and frequencies detected due to aliasing.
Yet another object is to provide a time interval measurement system in which a limited variance of a nominal or average sampling frequency, and an accumulation of multi-cycle durations to form sets of data corresponding to different cycle spans, lead to more rapid and more accurate measurements and characterization of jitter components in repetitive wave forms.
To achieve these and other objects, there is provided a process for generating a function with characteristics of an auto-correlation function indicating periodic jitter in a repetitive waveform, including:
a. timing a duration of a series of xe2x80x9cnxe2x80x9d consecutive periods in a repetitive waveform a plurality of times for a given xe2x80x9cn,xe2x80x9d where xe2x80x9cnxe2x80x9d is an integer, to generate a set of time values associated with the given xe2x80x9cn;xe2x80x9d
b. determining a variance value for the set of time values;
c. repeating steps (a) and (b) for a plurality of different values of xe2x80x9cn;xe2x80x9d and
d. generating an array of the variance values as a function of the values of xe2x80x9cn.xe2x80x9d
Note that one of the time value sets may be based on measuring one period, i.e. when n=1. The variance associated with each set of time values can be determiined according to the equation:                               Var          .                      [                          t              ⁡                              (                N                )                                      ]                          =                              (                          1              /              M                        )                    ⁢                                    ∑                              i                =                1                            M                        ⁢                                          [                                                      t                    ⁡                                          (                      N                      )                                                        -                                                            t                      _                                        ⁡                                          (                      N                      )                                                                      ]                            2                                                          (        1        )            
Where {overscore (t)} equals the average of the time values of the set, xe2x80x9cMxe2x80x9d equals the number of measurements in the set, and t(N) equals the time value for a particular measurement in the series from i=1 through i=M. As one example, each set of multi-cycle time values may consist of 100 individual time measurements, and sets may be provided over a range of 1,000 values of xe2x80x9cn,xe2x80x9d beginning at one cycle and incrementing the value of xe2x80x9cnxe2x80x9d by 1 for each succeeding set of time values.
The time measurements of consecutive cycles preferably are done according to a measurement rate uncorrelated to the jitter components of the waveform under study. More preferably the measurement rate is dithered about an average or nominal measurement rate. This insures that each set of time values yields a more random statistical sample, to insure a better measurement of variance.
According to another preferred analysis approach, the auto-correlation function derived by generating variance values as a function of xe2x80x9cnxe2x80x9d is mirrored to generate variance as a function of (xe2x88x92n), which exhibits the same behavior as the function based on positive n values. A second derivative of the mirrored function is generated, then multiplied by a window function, e.g. a triangular function. Then, a Fourier transform is performed to convert the time domain data into frequency domain data. The resulting function further can be subjected to a square root function to yield jitter as a function of frequency.
Yet another aspect of the present invention is a process for characterizing an angle (phase or frequency) modulating component in an angle modulated signal, including:
a. timing a duration of a series of xe2x80x9cnxe2x80x9d consecutive periods in a repetitive waveform for a plurality of times for a given n where n is an integer, to generate a set of measured time values associated with the given n;
b. generating a range value indicating a difference between the maximum measured time value and the minimum measured time value for the set of measured time values;
c. repeating steps (a) and (b) for a plurality of different values of n;
d. using the range values obtained in step (c) to generate a range array depicting the range of values as a function of the values of n;
e. differentiating the range array with respect to n; and
f. reconstructing the differentiated range array symmetrically around a designated location to provide a reordered array.
The reordered array, with appropriate scaling, can be interpreted as a time domain view of the modulating waveform, with a 180 degree phase ambiguity. Further resolution of the angle modulating component is achieved through the following additional steps:
g. integrating the reordered array to provide a simulated range array;
h. comparing the simulated array with the range array resulting from step (d);
i. selectively inverting portions of the reordered array resulting from step (f); and
j. repeating steps (g), (h), and (i) until a close correspondence is found between the simulated range array and the range array resulting from step (d).
As compared to the previously discussed technique based on variance values, recovering modulating signal characteristics based on range data is a more complex approach. At the same time, because range data contains phase information not contained in variance data, information based on ranges can provide a more detailed reconstruction of the modulating signal.
Another aspect of the present invention is a process for characterizing an angle (frequency or phase) modulating component in an angle modulated signal, including:
a. measuring a waveform multiple times at a measurement rate that varies about a nominal measurement rate, between a maximum measurement rate greater than the nominal rate and a minimum measurement rate less than the nominal rate;
b. based on said measuring, timing a duration of xe2x80x9cnxe2x80x9d consecutive periods of the waveform during each episode of said measuring, where xe2x80x9cnxe2x80x9d is an integer, to generate an array of time values, one time value associated with each measuring episode; and
c. processing the array of time values to generate an array of the time values as a function of frequency.
The preferred approach to generate the array of time values as a function of frequency, is to apply a Fourier transform to the initial array of time values.
In connection with measuring a waveform at a varying measurement rate, there is provided a more robust averaging method; namely, timing a duration of a series of xe2x80x9cnxe2x80x9d, s consecutive periods of a repetitive waveform, where n is an integer of at least two, to generate a multiple period time value, and then determining an average period by dividing the multiple time value by n.
As compared to conventional averaging methods used to reduce instrumentation noise, the multiple-period averaging approach requires less time, because fewer measurements are required. In particular, the present process requires just one measurement to generate one multiple-period time value, as opposed to the requirement under conventional averaging techniques, of averaging many single-period measurements to determine the mean. Under the conventional approach, the standard deviation of the mean is reduced in proportion to the square root of the number of measurements (each of a single cycle) used to generate an average in each set. By contrast, it has been found, surprisingly, that when the mean is determined according to a measured duration of a series of consecutive pulses, the standard deviation of the mean is reduced in proportion to the number of periods in the measurement, i.e. the value n.
Thus in accordance with the present invention, intrinsic noise or jitter is more rapidly determined and more accurately characterized, to facilitate the location of sources of noise within semiconductor circuits or other devices under test. The intrinsic noise due to the measurement system also is reduced, to afford greater accuracy in measurements and enhanced reliability.